{"paper":{"title":"Liouville quantum gravity weighted by conformal loop ensemble nesting statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Matthis Lehmkuehler, Nina Holden","submitted_at":"2022-04-21T06:27:15Z","abstract_excerpt":"We study Liouville quantum gravity (LQG) surfaces whose law has been reweighted according to nesting statistics for a conformal loop ensemble (CLE) relative to $n\\in \\mathbb{N}_0$ marked points $z_1,\\dots,z_n$. The idea is to consider a reweighting by $\\prod_{B\\subseteq \\{1,\\dots,n\\}} e^{\\sigma_B N_B}$, where $\\sigma_B\\in\\mathbb{R}$ and $N_B$ is the number of CLE loops surrounding the points $z_i$ for $i\\in B$. This is made precise via an approximation procedure where as part of the proof we derive strong spatial independence results for CLE. The reweighting induces logarithmic singularities f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.09905","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.09905/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}